Doug Kerr
Well-known member
We often hear of a certain severity of flooding described as a "100-year flood". Just what does that mean?
A common "explanation" is that "this is the severity of a flood that we could expect to be met or exceeded only every 100 years." But a little thought will reveal that this hasn't really said something definite.
And in fact the term "100-year flood" does not have an inherent meaning in the world of statistics and probability.
Often a definition is given in connection with a regulation or specification that will use the term, and of course there are as many of these as there are specification writers.
But perhaps the most common definition is this:
Well-written specifications and regulations may call this a "1% annual chance" flood, staying away from the meaningless "100-year" term.
Now, based on that definition, what is the probability that, in any 100-year period, we will have at least one flood of that severity or greater. Well, it's 0.634 (63.4%). Ooh!
Then how long a period would we have to have in which there would be a 100% probability that the severity criterion would be met at least once. Well, no period would be long enough for that.
How about 1000 years? The probability of having a within that period a flood (or more) that met or exceeded the severity criterion is:
99.99568%
Close to 100%, but not 100%.
How about 10,000 years? Well, I'd have to start my answer with 44 9's!
In any case, is there anything "100-year" about the "100-year flood"? Well, yes.
An important statistical parameter is the statistical expectation of some randomly-varying value. The concept is this: if we looked at a city's "daily police blotter" for a zillion days. and found the average of the reported number of robberies for the day over all those days, that value would be "the statistical expectation of the number of robberies in a day". We can also call that number (in this context) the expected number of robberies in a day.
Now, what about our "100-year flood? Again, if the term is taken to have the definition I gave above, it turns out that the expected number of floods of that severity or greater in any 100-year period is - - - one!
Again, what does that mean? Well, if we could let a 100-year period play out a zillion times (perhaps in a zillion alternate universes), and for each "play" counted the number of floods during the 100 years that met or exceeded the defined severity, the average of that count over the zillion "plays" of the year would be one.
So, if we wanted a "homey", but accurate presentation of the definition of 100-year flood I stated above, it would be:
Doug
A common "explanation" is that "this is the severity of a flood that we could expect to be met or exceeded only every 100 years." But a little thought will reveal that this hasn't really said something definite.
And in fact the term "100-year flood" does not have an inherent meaning in the world of statistics and probability.
Often a definition is given in connection with a regulation or specification that will use the term, and of course there are as many of these as there are specification writers.
But perhaps the most common definition is this:
The severity of a flood such that the probability of its being met or exceeded at least once in any one-year period is 0.01 (one in 100).
Well-written specifications and regulations may call this a "1% annual chance" flood, staying away from the meaningless "100-year" term.
Now, based on that definition, what is the probability that, in any 100-year period, we will have at least one flood of that severity or greater. Well, it's 0.634 (63.4%). Ooh!
Then how long a period would we have to have in which there would be a 100% probability that the severity criterion would be met at least once. Well, no period would be long enough for that.
How about 1000 years? The probability of having a within that period a flood (or more) that met or exceeded the severity criterion is:
99.99568%
Close to 100%, but not 100%.
How about 10,000 years? Well, I'd have to start my answer with 44 9's!
In any case, is there anything "100-year" about the "100-year flood"? Well, yes.
An important statistical parameter is the statistical expectation of some randomly-varying value. The concept is this: if we looked at a city's "daily police blotter" for a zillion days. and found the average of the reported number of robberies for the day over all those days, that value would be "the statistical expectation of the number of robberies in a day". We can also call that number (in this context) the expected number of robberies in a day.
Now, what about our "100-year flood? Again, if the term is taken to have the definition I gave above, it turns out that the expected number of floods of that severity or greater in any 100-year period is - - - one!
Again, what does that mean? Well, if we could let a 100-year period play out a zillion times (perhaps in a zillion alternate universes), and for each "play" counted the number of floods during the 100 years that met or exceeded the defined severity, the average of that count over the zillion "plays" of the year would be one.
So, if we wanted a "homey", but accurate presentation of the definition of 100-year flood I stated above, it would be:
The severity of a flood such that for over many 100-year periods, on the average there would be one flood of that severity or greater in the period.
Best regards,Doug
